Wednesday, November 16, 2011

Gambler's fallacy

I was listening to ESPN First Take on Monday (podcast [mp3]) and the hosts were debating whether the Falcons should have punted or not on fourth and short in overtime against the Saints. In wrapping up the debate, Jay Crawford said (around minute 32 of the podcast):

"One thing on your [Jon Ritchie's] numbers deal, because I'm a math guy too. They [the Falcons] have gone for it twice earlier, similar situation, you said that there is a 66.1% probability [sic] of picking it up ... Here's why you don't go for it: they've tried it twice, they've made it twice [earlier in the game], it's probability. Because if you're sitting at a blackjack table and you're playing odds, you're playing three times, and the law of your averages tells you, it's simple math if you try it three times you're going to make it twice and miss it once, and that's exactly how it played out."

2 comments:

Maybe he should delve into Bayesian probability instead? Given that they have gone for it twice before in that game (with some particular results), what is the probability that they will make the third one? In other words, what has history told them about the third attempt with the specific results on the first two attempts?

Probably not :). Although allowing for conditional probabilities nullifies the gambler's fallacy, the problem of deciding what past events are relevant is really hard, much less assigning probabilities to them. But if you had such a (Markov) model then you could make more accurate statements about the probability of specific events.